When wrapping objects in paper or plastics it is as a rule necessary to either lift or somehow turn the object on a working table top. This operation is an easy one only if the object has a cylindrical or almost cylindrical shape. On the other hand, if the object is more irregular or angular in shape it becomes a great deal more complicated to wrap the object. For instance, in order to apply a wrapping around a hearty box or a box-shaped bale of straw, the box or bale must first be lifted and placed in position on the wrapping sheet by means of a lifting aid whereupon the wrapping sheet is wound around the object to allow the package to be closed. An alternative way of applying the wrapping is to roll the object to which one end of the wrapping material has been attached, on the table top in such a manner that the wrapping covers the object. The wrapping is then closed about the object. However, rolling of the often angular or square object on the support is a hard and often laborious task, particularly if it is done manually. One solution to mechanize the wrapping procedure is to clamp the object in position at its short ends and to thereafter rotate the object so as to apply the wrapping about it. The object must then be deposited on a working top to allow closing at the short ends. This procedure is a time-consuming one.